Euler capital allocation

Naming pattern: Measures with "Euler” behavior follow the name pattern:Main Measure Name Euler.

Euler is one of the approaches implemented in the FRTB Accelerator to decompose a non-linear measure down to additive components. For instance, the Euler variation of the IMCC measure is called IMCC (Euler): the latter enables you to allocate a result (for instance, at firm level) down to individual components (typically, desks).

Overview of Euler Calculations

The theory behind Euler Calculations is based on these facts:

• Use of Euler’s theorem of homogeneous functions

• Capital Charges are homogeneous functions of degree 1

• Euler Capital Allocation is the evaluation of the derivative on a sub-portfolio

Analytical vs Numerical Euler

The difference between Analytical and Numerical Euler is in how the calculations are performed:

• For Analytical Euler, we differentiate the functions and evaluate the derivative (this gives the exact value).

• For Numerical Euler, we use the Existing Capital Charge calculations to numerically approximate the derivative.

Follow this link to see the measures with the described behavior: Euler Measures.